1. Field of the Invention
This invention relates to magnetic resonance imaging and, more particularly, to a method and corresponding apparatus for capturing and providing MRI data suitable for use in a multi-dimensional imaging processes.
2. Background of the Invention
Magnetic resonance imaging (MRI) is a well known method of non-invasively obtaining images representative of internal physiological structures. In fact, there are many commercially available approaches and there have been numerous publications describing various approaches to MRI. Although MRI will be described herein as applying to a person's body, it may be applied to visualize the internal structure of other objects as well, and the invention is not limited to application of MRI in a human body.
A conventional MRI system is schematically illustrated in FIG. 1. As shown in FIG. 1, an MRI system 10 includes a static magnet assembly, gradient coils, and transmit RF coils collectively denoted 12 under control of a processor 14, which typically communicates with an operator via a conventional keyboard/control workstation 16. These devices generally employ a system of multiple processors for carrying out specialized timing and other functions in the MRI system 10. Accordingly, as depicted in FIG. 1, an MRI image processor 18 receives digitized data representing radio frequency nuclear magnetic resonance responses from an object region under examination and, typically via multiple Fourier transformation processes well-known in the art, calculates a digitized visual image (e.g., a two-dimensional array of picture elements or pixels, each of which may have different gradations of gray values or color values, or the like) which is then conventionally displayed, or printed out, on a display 18a. 
A plurality of surface coils 20a, 20b . . . 20i may be provided to simultaneously acquire NMR signals for simultaneous signal reception, along with corresponding signal processing and digitizing channels.
A conventional MRI device establishes a homogenous magnetic field, for example, along an axis of a person's body that is to undergo MRI. This magnetic field conditions the interior of the person's body for imaging by aligning the nuclear spins of nuclei, in atoms and molecules forming the body tissue, along the axis of the magnetic field. If the orientation of the nuclear spin is perturbed out of alignment with the magnetic field, the nuclei attempt to realign their nuclear spins with an axis of the magnetic field. Perturbation of the orientation of nuclear spins may be caused by application of a radiofrequency (RF)-pulses. During the realignment process, the nuclei precess about the axis of the magnet field and emit electromagnetic signals that may be detected by one or more coils placed on or about the person.
It is known that the frequency of the nuclear magnetic radiation (NMR) signal emitted by a given precessing nucleus depends on the strength of the magnetic field at the nucleus' location. Thus, as is well known in the art, it is possible to distinguish radiation originating from different locations within the person's body simply by applying a field gradient to the magnetic field across the person's body. For sake of convenience, this will be referred to as the left-to-right direction. Radiation of a particular frequency can be assumed to originate at a given position within the field gradient, and hence at a given left-to-right position within the person's body. Application of a such a field gradient is referred to herein as frequency encoding.
The simple application of a field gradient does not allow two dimensional resolution, however, since all nuclei at a given left-to-right position experience the same field strength, and hence emit radiation of the same frequency. Accordingly, application of a frequency-encoding gradient, alone, does not make it possible to discern radiation originating from the top vs. radiation originating from the bottom of the person at a given left-to-right position. Resolution has been found to be possible in this second direction by application of gradients of varied strength in a perpendicular direction to thereby perturb the nuclei in varied amounts. Application of such additional gradients is referred to herein as phase encoding.
Frequency-encoded data sensed by the coils during a phase encoding step is stored as a line of data in a data matrix known as the k-space matrix. Multiple phase encoding steps must be performed to fill the multiple lines of the k-space matrix. An image may be generated from this matrix by performing a Fourier transformation of the matrix to convert this frequency information to spatial information representing the distribution of nuclear spins or density of nuclei of the image material.
MRI has proven to be a valuable clinical diagnostic tool for a wide range of organ systems and pathophysiologic processes. Both anatomic and functional information can be gleaned from the data, and new applications continue to develop as the technology and techniques for filling the k-space matrix improve. As technological advances have improved achievable spatial resolution, for example, increasingly finer anatomic details have been able to be imaged and evaluated using MRI.
Often, however, there is a tradeoff between spatial resolution and imaging time, since higher resolution images require a longer acquisition time. This balance between spatial and temporal resolution is particularly important in cardiac MRI, where fine details of coronary artery anatomy, for example, must be discerned on the surface of a rapidly beating heart. A high-resolution image acquired over a large fraction of the cardiac cycle will be blurred and distorted by bulk cardiac motion, whereas a very fast image may not have the resolution necessary to trace the course and patency of coronary arteries.
Imaging time is largely a factor of the speed with which the MRI device can fill the k-space matrix. In conventional MRI, the k-space matrix is filled one line at a time. Although many improvements have been made in this general area, the speed with which the k-space matrix may be filled is limited by, e.g., the intervals necessary to create, switch or measure the magnetic fields or RF signals involved in data acquisition, as well as physiological limits on the maximum strength and variation of magnetic fields and RF signals the human body is able to withstand.
To overcome these inherent limits, several techniques have been developed to simultaneously acquire multiple lines of data for each application of a magnetic field gradient. These techniques, which may collectively be characterized as “parallel imaging techniques,” use spatial information from arrays of RF detector coils to substitute for encoding which would otherwise have to be obtained in a sequential fashion using field gradients and RF pulses. The use of multiple effective detectors has been shown to multiply imaging speed, without increasing gradient switching rates or RF power deposition.
The first in vivo images using the parallel MR imaging approach were obtained using the SMASH (SiMultaneous Acquisition of Spatial Harmonics) technique. The history of parallel imaging in general and of the SMASH technique in particular is described in greater detail in U.S. Pat. No. 5,910,728, the content of which is hereby incorporated by reference. An alternative strategy for parallel imaging, known as “subencoding”, had been described earlier using phantom images only. A technique closely related to subencoding—the SENSE (SENSitivity Encoding) technique—has recently been described and applied to in vivo imaging. The SENSE technique is discussed in more detail in International Publication Number WO 99/54746, the content of which is hereby incorporated by reference.
Parallel imaging techniques have tended to fall into one of two general categories, as exemplified by the SMASH and the subencoding/SENSE methods, respectively. SMASH operates primarily on the k-space matrix and is referred to herein as operating in “k-space.” Subencoding/SENSE, by contrast, operate primarily on data that has been transformed via one or more Fourier transforms into image data, and will be referred to herein as operating in the “image domain.”
SMASH
SMASH uses spatial information from an array of RF coils to obtain one or more lines of k-space data traditionally generated using magnetic field gradients, thereby allowing multiple phase encoding steps to be performed in parallel rather than in a strictly sequential fashion. To date, this parallel data acquisition strategy has resulted in up to five-fold accelerations of imaging speed and efficiency in vivo, and has enabled up to eight-fold accelerations in phantoms using specialized hardware.
SMASH is based on the principle that combinations of signals from component coils in an array may be formed to mimic the sinusoidal spatial modulations (or “spatial harmonics”) imposed by field gradients, and that these combinations may be used to take the place of time-consuming gradient steps. Spatial harmonic fitting is a fundamental step in SMASH image reconstructions. This fitting procedure is designed to yield the linear combinations of coil sensitivity functions Cl(x,y) which most closely approximate various spatial harmonics of the field of view (FOV):                                           ∑                          l              =              1                                      L              ′                                ⁢                                    n              l                              (                m                )                                      ⁢                                          C                l                            ⁡                              (                                  x                  ,                  y                                )                                                    ≈                              C            0                    ⁢                                           ⁢                      exp            ⁡                          (                              ⅈ                ⁢                                                                   ⁢                m                ⁢                                                                   ⁢                Δ                ⁢                                                                   ⁢                                  k                  y                                ⁢                y                            )                                                          (        1        )            Here, m is an integer indicating the order of the spatial harmonic, l is a coil index running from 1 to the number of coils L, nl(m) are complex fitting coefficients, and Δky=2π/FOV.
FIGS. 2 and 3 demonstrate the spatial harmonic fitting procedure schematically for a set of eight rectangular coils 20a, 20b . . . 20h laid end-to-end, with a slight overlap. As shown in FIG. 3a, each coil 20a, 20b . . . has a sensitivity curve a, b . . . which rises to a broad peak directly under the coil and drops off substantially beyond the coil perimeter. The sum of the coil sensitivities form a relatively constant sensitivity, over the width of the array, corresponding to the zeroth spatial harmonic. FIGS. 3a-3e illustrate recombinations of different ones of these individual offset but otherwise similar coil sensitivity functions into a new synthetic sinusoidal spatial sensitivity. Different weightings of the individual component coil sensitivities lead to net sensitivity profiles approximating several spatial harmonics. Coil sensitivities (modeled schematically for FIGS. 3a-3e as Gaussian in shape, though in practice their shapes are somewhat more complicated and they may have both real and imaginary components) may thereby be combined to produce harmonics at various fractions of the fundamental spatial wavelength λy=2π/Ky, with λy being on the order of the total coil array extent in y. Weighted individual coil sensitivity profiles are depicted as thin solid lines beneath each component coil. Dashed lines represent the sinusoidal or consinusoidal weighting functions. Combined sensitivity profiles are indicated by thick solid lines. These combined profiles closely approximate ideal spatial harmonics across the array. A total of five spatial harmonics are shown here, but in general the maximum number of such independent combinations which may be formed for any given array is equal to the number of array elements (in this case, eight).
Once fitting coefficients satisfying Eq. (1) have been identified, a similar weighting of measured MR signals Sl(kx,ky) from an image plane with spin density ρ(x,y) yields composite signals shifted by an amount −mΔky in k-space:                                                                                           ∑                                      l                    =                    1                                    L                                ⁢                                                      n                    l                                          (                      m                      )                                                        ⁢                                                            S                      l                                        ⁡                                          (                                                                        k                          x                                                ,                                                  k                          y                                                                    )                                                                                  =                            ⁢                                                ∑                                      l                    =                    1                                    L                                ⁢                                                      n                    l                                          (                      m                      )                                                        ⁢                                      ∫                                          ∫                                                                        ⅆ                          x                                                ⁢                                                  ⅆ                          y                                                ⁢                                                                                                   ⁢                                                                              C                            l                                                    ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                                                                   ⁢                                                  ρ                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                                                                   ⁢                                                  exp                          ⁡                                                      (                                                                                                                            -                                  ⅈ                                                                ⁢                                                                                                                                   ⁢                                                                  k                                  x                                                                ⁢                                x                                                            ,                                                                                                -                                  ⅈ                                                                ⁢                                                                                                                                   ⁢                                                                  k                                  y                                                                ⁢                                y                                                                                      )                                                                                                                                                                                                                      =                            ⁢                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                                   ⁢                                          (                                                                        ∑                                                      l                            =                            1                                                    L                                                ⁢                                                                              n                            l                                                          (                              m                              )                                                                                ⁢                                                                                    C                              l                                                        ⁡                                                          (                                                              x                                ,                                y                                                            )                                                                                                                          )                                        ⁢                                          ρ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                                                                   ⁢                                          exp                      ⁡                                              (                                                                                                            -                              ⅈ                                                        ⁢                                                                                                                   ⁢                                                          k                              x                                                        ⁢                            x                                                    ,                                                                                    -                              ⅈ                                                        ⁢                                                                                                                   ⁢                                                          k                              y                                                                                                      )                                                                                                                                                                    ≈                            ⁢                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                                   ⁢                                          C                      0                                        ⁢                                                                                   ⁢                                          exp                      ⁡                                              (                                                  ⅈ                          ⁢                                                                                                           ⁢                          m                          ⁢                                                                                                           ⁢                          Δ                          ⁢                                                                                                           ⁢                                                      k                            y                                                    ⁢                          y                                                )                                                              ⁢                                                                                   ⁢                                          ρ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                                                                   ⁢                                          exp                      ⁡                                              (                                                                                                            -                              ⅈ                                                        ⁢                                                                                                                   ⁢                                                          k                              x                                                        ⁢                            x                                                    ,                                                                                    -                              ⅈ                                                        ⁢                                                                                                                   ⁢                                                          k                              y                                                        ⁢                            y                                                                          )                                                                                                                                                                    =                            ⁢                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                                   ⁢                                          C                      0                                        ⁢                                                                                   ⁢                                          ρ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                                                                   ⁢                                          exp                      ⁡                                              (                                                                                                            -                              ⅈ                                                        ⁢                                                                                                                   ⁢                                                          k                              x                                                        ⁢                            x                                                    ,                                                                                    -                                                              ⅈ                                ⁡                                                                  (                                                                                                            k                                      y                                                                        -                                                                          m                                      ⁢                                                                                                                                                           ⁢                                      Δ                                      ⁢                                                                                                                                                           ⁢                                                                              k                                        y                                                                                                                                              )                                                                                                                      ⁢                            y                                                                          )                                                                                                                                                                    =                            ⁢                                                S                  composite                                ⁡                                  (                                                            k                      x                                        ,                                                                  k                        y                                            -                                              m                        ⁢                                                                                                   ⁢                        Δ                        ⁢                                                                                                   ⁢                                                  k                          y                                                                                                      )                                                                                        (        2        )            
This k-space shift has precisely the same form as the phase-encoding shift produced by evolution in a field gradient of magnitude γGt=−mΔky (where γ is the gyromagnetic ratio, G the magnitude of the gradient, and t the time spent in the gradient). Thus, the coil-encoded composite signals may be used to take the place of omitted gradient steps, thereby reducing the data acquisition time by multiplying the amount of spatial information gleaned from each phase encoding step. SMASH takes its cue from the physical model of gradient phase encoding, transforming the localized coil sensitivities into extended composite phase modulations (Eq. (1)) which can serve as supplementary effective gradient sets operating in tandem with the applied field gradients.
Several of the steps in the SMASH reconstruction procedure are summarized in FIGS. 4a-4c and 5a-5c, which illustrate a SMASH reconstruction with acceleration factor M=2 using a 3-element RF coil array. FIGS. 4a-4c show a k-space schematic, and FIGS. 5a-5c show image data from a water phantom at each of the corresponding stages of reconstruction. With the necessary weights in hand, MR signal data are acquired simultaneously in the coils of the array. A fraction 1/M of the usual number of phase encoding steps are applied with M times the usual spacing in k-space (FIG. 4a). The component coil signals acquired in this way correspond to aliased images with a fraction 1/M of the desired field of view (FIG. 5a). With 1/M times fewer phase encoding steps, only a fraction 1/M of the time usually required for this FOV is spent on data collection. Next, the appropriate M linear combinations of the component coil signals are formed, to produce M shifted composite signal data sets (FIG. 4b). The composite signals are then interleaved to yield the full k-space matrix (FIG. 4c,), which is Fourier transformed to give the reconstructed image (FIG. 5c). It should be noted that the combination of component coil signals into composite shifted signals may be performed in real time as the data arrives, or after the fact via postprocessing as is appropriate or convenient with the apparatus and the calibration information at hand.